Analytic inversion of remote-sensing data

C. D. Capps; R. L. Henning; G. M. Hess

doi:10.1364/AO.21.003581

Applied Optics
Vol. 21,
Issue 19,
pp. 3581-3587
(1982)
•https://doi.org/10.1364/AO.21.003581

Analytic inversion of remote-sensing data

C. D. Capps, R. L. Henning, and G. M. Hess

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C. D. Capps, R. L. Henning, and G. M. Hess, "Analytic inversion of remote-sensing data," Appl. Opt. 21, 3581-3587 (1982)

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Abstract

An analytic method for inversion problems of the Fredholm integral type is developed. The application of this formalism to error analysis and optimal experimental design is discussed. Finally, results from this method for a simulated experiment are compared with other commonly used inversion techniques.

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Kernel index	Wavelength (μm)	g_i
1	0.266	0.5187
2	0.524	0.6114
3	0.782	0.6419
4	1.04	0.6665
5	1.55	0.5910
6	2.33	0.4914
7	2.59	0.5650
8	2.85	0.3937
9	3.63	0.8542
10	3.88	1.1800
11	4.14	1.3350
12	4.91	0.9833

1.0000	0.6339	0.7005	0.7307	0.7674	0.6381	0.8188	0.7589	0.4768	0.4472	0.4784	0.7793
	1.0000	0.7350	0.7677	0.7815	0.7280	0.7372	0.7625	0.6395	0.5842	0.5208	0.7449
		1.0000	0.8781	0.8507	0.8452	0.7995	0.8197	0.7534	0.6761	0.5563	0.7731
			1.0000	0.9156	0.9130	0.8496	0.8468	0.8007	0.7260	0.5932	0.8095
				1.0000	0.8103	0.8915	0.9085	0.6847	0.5922	0.5195	0.8403
					1.0000	0.7280	0.7537	0.8385	0.7303	0.5007	0.6714
						1.0000	0.8559	0.4965	0.4872	0.5570	0.9139
							1.0000	0.6570	0.4636	0.3392	0.7480
								1.0000	0.9103	0.6262	0.3660
									1.0000	0.8750	0.6672
										1.0000	0.8007
											1.0000

	Eigenvector

Kernel	1	2	3	4	5	6	7	8	9	10	11	12
1	0.268	−0.285	0.252	−0.492	0.712	0.144	0.041	0.116	0.024	0.019	−0.005	0.000
2	0.282	−0.090	−0.026	0.838	0.396	0.194	0.076	0.093	0.070	0.015	0.001	0.000
3	0.306	−0.039	−0.157	−0.121	−0.260	0.123	0.876	0.123	0.044	0.014	0.005	0.000
4	0.321	−0.024	−0.155	−0.107	−0.209	0.141	−0.303	0.204	0.786	−0.205	0.019	0.002
5	0.313	−0.196	−0.051	0.006	−0.215	−0.280	−0.233	0.715	−0.389	0.139	0.037	−0.003
6	0.299	0.057	−0.370	−0.120	−0.077	0.603	−0.242	−0.222	−0.434	−0.190	0.229	−0.004
7	0.300	−0.291	0.248	0.019	−0.281	0.126	−0.132	−0.368	0.051	0.686	−0.192	−0.064
8	0.293	−0.325	−0.193	0.024	0.023	−0.581	0.004	−0.428	0.009	−0.166	0.417	0.217
9	0.273	0.273	−0.404	−0.080	0.210	−0.315	−0.036	−0.131	−0.014	0.113	−0.332	−0.572
10	0.261	0.554	−0.009	−0.056	0.100	−0.078	−0.035	−0.009	−0.106	0.189	−0.185	0.731
11	0.235	0.479	0.528	0.025	−0.061	−0.034	0.019	0.011	0.015	0.036	0.586	−0.293
12	0.302	−0.037	0.454	0.063	−0.189	−0.073	−0.019	−0.155	−0.177	−0.595	−0.496	−0.030

i	10 eigenvectors	5 eigenvectors
1	0.835	0.835
2	0.847	0.847
3	0.624	0.624
4	0.058	0.058
5	0.041	0.410
6	−0.326
7	0.084
8	0.034
9	0.052
10	−0.103

i	1% Error	10% Error
1	0.5194	0.5262
2	0.6105	0.6026
3	0.6401	0.6238
4	0.6614	0.6151
5	0.5922	0.6029
6	0.4943	0.5201
7	0.5659	0.5742
8	0.3964	0.4209
9	0.8576	0.8888
10	1.1975	1.3563
11	1.3224	1.2090
12	0.9761	0.9116

Abstract

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Tables (5)

Equations (24)

Applied Optics